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Maidana, Manuel Augusto. "Desarrollo de un modelo numérico 3D en elementos finitos para las ecuaciones de Navier-Stokes : aplicaciones oceanográficas." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/457520.
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En esta tesis se ha desarrollado y validado un modelo tridimensional de circulación costera en elementos finitos capaz de simular una región limitada del océano. La escala de longitud de las aplicaciones pueden ser del orden del ancho de la plataforma continental o menores y la escala de tiempo entre el período de las ondas de las mareas y de las ondas debidas al viento.
La formulación del modelo, denominado HELIKE, está basada en las tres componentes de la ecuación de Navier-Stokes (no-hidrostáticas) y tiene en cuenta las dos componentes de la aceleración de Coriolis, (componentes normal y tangencial a la superficie terrestre), gradientes de densidad, turbulencia (valores constantes o modelos de turbulencia como Smagorinsky, Munk-Anderson o Pacanowski-Philander), fricción con fondo, tensión de viento y superficie libre. Pudiéndose también utilizar el modelo en fondos con batimetrías irregulares (fondo no-horizontal).
Los modelos tridimensionales no-hidrostáticos como el desarrollado en esta tesis están bien planteados para dominios con contorno abierto. Esto es muy importante en el modelado de mesoescala donde el modelado de la pequeña, pero relevante, velocidad vertical es importante y los contornos abiertos son inevitables. La formulación no-hidrostática tiene fundamentalmente importancia cuando la escala horizontal del movimiento se hace comparable con su escala vertical y no se pueda despreciar la velocidad vertical como por ejemplo, se da el caso en la circulación sobre fondos abruptos, convección en el océano abierto, etc.
El uso combinado de una discretización espacial por el método de los elementos finitos y el uso de mallas no-estructuradas proveen al modelo una gran flexibilidad para adaptarse a la complicada geometría de la línea de costa y del fondo marino. Además de la posibilidad de realizar refinamientos de la malla sobre áreas de mayor interés y aplicar las condiciones de contorno apropiadas para cada caso.<br>In this thesis finite element model was developed, named HELIKE, for the numerical simulation of the three-dimensional, turbulent, non-hydrostatic, free-surface flows like those arising in the study of the motion of water in coastal regions. The kinematic free-surface equation is used to compute the surface elevation, without resorting to vertical averages. The model developed here incorporates surface wind stress, bottom friction, Coriolis acceleration, the baroclinic term to take account the density gradients, and it is applicable to irregular bottom topographies. A pressure stabilization technique is employed to stabilize the finite element solution. Numerical results confirm the accuracy, robustness and applicability of the proposed method.
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Ghosh, Amrita. "Naviers-Stokes equations with Navier boundary condition." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3021/document.
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Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bord<br>My PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up
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GALLANA, LUCA. "Statistical analysis of inhomogeneous fluctuation fields. Scalar transport in shearless turbulent mixing, effects of stratification, solar wind and solar wind-interstellar medium interaction." Doctoral thesis, Politecnico di Torino, 2016. http://hdl.handle.net/11583/2653026.
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Turbulence is a condition that can occur in a broad range of fluids, which may belong to very different physical environments, each with their own unique characteristics. Mathematical and analytical studies are generally limited by the high degree of complexity of the system, therefore, numerical/laboratory experiments and in-situ measurements play a fundamental role in the study of these phenomena.
An analysis on two different anisotropic fluctuating fluid fields has been performed: both flows, while belonging to different physical contexts, are characterized by the presence of multiscale inhomogeneous fluctuations, to which is associated a strong anisotropy, and by the presence of effects related to stratification / mixing.
The first is one of the most simple anisotropic turbulent flow, namely the shearless turbulent mixing, and it has been studied by means of direct numerical simulation of Navier-Stokes equations, with the aim of characterize the passive scalar transport and the effects related to the presence of a thermal stratification. The second is a more complex fluid field, that is the solar wind, which belong to magnetohydrodynamic flows; the analysis on solar wind have been performed taking advantage of in-situ measurement of the Voyager 2 spacecraft, trying to provide a statistical and spectral characterization despite the presence of gaps in the recorded time-series.
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Cai, Zhemin. "A High-order Discontinuous Galerkin Method for Simulating Incompressible Fluid-Thermal-Structural Problems." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/20961.
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The use of discontinuous Galerkin (DG) methods to solve fluid thermal structure interaction problems in numerical modelling is known to offer several advantages. In particular, DG methods provide the flexibility of using different approximations in different elements, which makes the methods ideal for hp-adaptivity. The first objective of this thesis is to present a framework for the computation of fluid thermal structure interaction problems within both the single and multi-solid domain using DG methods on unstructured grids. The full solver consists of four main components: the incompressible fluid solver, the conjugate heat transfer solver, the linear elastic solver and the fluid to structure interaction solver. Based on an earlier developed DG solver for the incompressible Navier-Stokes equation, the fluid advection-diffusion equation, the Boussinesq term, the solid heat equation and the linear elastic equation are introduced using an explicit DG formulation. A Dirichlet-Neumann partitioning strategy has been implemented to achieve the data exchange process via the numerical flux of interface quadrature points in the fluid-solid interface. Formal h and p convergence studies employing the method of manufactured solutions demonstrate that the expected order of accuracy is achieved. Computational effort is documented in detail demonstrating precisely that for all cases the highest order accurate algorithm has several magnitudes lower error than lower-order schemes for a given computational effort. Secondly, this thesis has proposed a detailed compact thermoelectric cooler (TEC) modelling method based on an existing black box like compact TEC model. Close comparisons validate that both the detailed and the black box like compact model are accurate enough to simulate the conduction only case. When air convection is required to carry out a system-level thermal management optimization, the detailed compact modelling method is more reliable.
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BORDIGNON, ALEX LAIER. "NAVIER-STOKES EM GPU." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2006. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8928@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Nesse trabalho, mostramos como simular um fluido em duas
dimensões em um domÃnio com fronteiras arbitrárias. Nosso
trabalho é baseado no esquema stable fluids desenvolvido
por Joe Stam. A implementação é feita na GPU (Graphics
Processing Unit), permitindo velocidade de interação com o
fluido. Fazemos uso da linguagem Cg (C for Graphics),
desenvolvida pela companhia NVidia. Nossas principais
contribuições são o tratamento das múltiplas fronteiras,
onde aplicamos interpolação bilinear para atingir melhores
resultados, armazenamento das condições de fronteira usa
apenas um canal de textura, e o uso de confinamento de
vorticidade.<br>In this work we show how to simulate fluids in two
dimensions in a domain with arbitrary bondaries. Our work
is based on the stable fluid scheme developed by Jo Stam.
The implementation is done in GPU (Graphics Processinfg
Unit), thus allowing fluid interaction speed. We use the
language Cg (C for Graphics) developed by the company
Nvídia. Our main contributions are the treatment of
domains with multiple boundaries, where we apply bilinear
interpolation to obtain better results, the storage of the
bondaty conditions in a unique texturre channel, and the
use of vorticity confinement.
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Rejaiba, Ahmed. "Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3050/document.
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Résumé : Cette thèse est consacrée à l'étude des équations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier dans un ouvert borné de . Le manuscrit ici est composé de trois chapitres. Dans le premier, nous considérons les équations de Stokes stationnaires avec des conditions aux limites de Navier. Nous démontrons l'existence, l'unicité et la régularité de la solution d'abord dans un cadre hilbertien puis dans le cadre de la théorie . Nous traitons aussi le cas de solutions très faibles. Dans le deuxième chapitre, nous nous intéressons aux équations de Navier-Stokes avec la condition de Navier. Sous certaines hypothèses sur les données, nous démontrons l'existence de solution faible dans , avec en utilisant un théorème du point fixe appliqué à un problème d'Oseen. Nous démontrons examinons ensuite les questions de régularité des solutions en particulier dans . Dans le dernier chapitre, nous étudions le problème d'évolution de Stokes avec la condition de Navier. La résolution de ce problème se fait au moyen de la théorie des semi-groupes analytiques qui jouent un rôle important pour établir l'existence et l'unicité de la solution dans le cas homogène. Nous traitons le cas du problème non homogène par le biais des puissances imaginaires de l'opérateur de Stokes<br>This thesis is devoted to the study of the Stokes equations and Navier-Stokes equations with Navier boundary conditions in a bounded domain of . The work contains three chapters: In the first chapter, we consider the stationary Stokes equations with Navier boundary condition. We show the existence, uniqueness and regularity of the solution in the Hilbert case and in the -theory. We prove also the case of very weak solutions. In the second chapter, we focus on the Navier-Stokes equations with the Navier boundary condition. We show the existence of the weak solution in , with by a fixed point theorem over the Oseen equation. We show also the existence of the strong solution in . In chapter three, we study the evolution Stokes problem with Navier boundary condition. For this, we apply the analytic semi-groups theory, which plays a crucial role in the study of existence and uniqueness of solution in the case of the homogeneous evolution problem. We treat the case of non-homogeneous problem through imaginary powers of the Stokes operator
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Cannone, Marco. "Ondelettes, paraproduits et Navier-Stokes." Paris 9, 1994. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1994PA090016.
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Dans cette thèse nous donnons quelques théorèmes d'existence et unicité de solutions mild du problème de Cauchy associe aux équations de Navier-Stokes. Dans la première partie, inspirés par une approche en ondelettes établie par P. Federbush, nous utilisons la décomposition de Littlewood-Paley pour en déduire un théorème d'existence et unicité locale de solutions mild à valeurs dans un espace de Banach abstrait de distributions. Nombreux exemples de tels espaces seront fournis, comme ceux de Lebesgue, Sobolev, Morrey-Campanato et Besov. La deuxième partie de la thèse est consacrée aux solutions globales mild dans des espaces de Banach dont la norme est invariante par les dilatations normalisées. En particulier, nous généralisons un résultat classique du a t. Kato en faisant remarquer que le temps de vie de sa solution globale est, en effet, donne par une norme Besov plus faible que celle usuelle de Lebesgue ne le laissait prévoir. Enfin, nous montrons comment utiliser lesdits espaces de Besov pour en déduire un théorème d'existence et unicité de solutions auto-similaires pour les équations de Navier-Stokes
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Mallinger, François. "Couplage adaptatif Boltzmann Navier-Stokes." Paris 9, 1996. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1996PA090042.
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Nous étudions les écoulements externes en régime semi raréfié à grands nombre de mach. Pour ce faire, nous proposons une stratégie de décomposition de domaine couplant les modèles Boltzmann et Navier-Stokes. Le couplage est réalisé par le biais de conditions aux limites. Les domaines de calcul Boltzmann et Navier-Stokes sont déterminés de manière automatique par un critère analysant la validité de la solution Navier-Stokes. Nous proposons donc un algorithme de couplage adaptatif qui prend en compte d'une part la détermination automatique des domaines, et d'autre part un algorithme de marche en temps pour le couplage des modèles. Le couplage adaptatif résulte d'une interprétation cinétique des équations de Navier-Stokes. Pour le généraliser, nous étudions la transition entre régimes microscopiques (Boltzmann) and macroscopiques (Navier-Stokes) pour des gaz diatomiques, en étendant la démarche initiale de grad. Enfin nous donnons une justification mathématique du couplage Boltzmann Navier-Stokes<br>We study external flows for semirarefied régimes at high mach number. We propose a domain décomposition strategy coupling Boltzmann and Navier-Stokes models. The coupling is done by boundary conditions. The Boltzmann and Navier-Stokes computational domains are defined automatically thanks to a critérium analysing the validity of the numerical Navier-Stokes solution. We propose therefore an adaptative coupling algorithm taking into account both the automatic définition of the computation domains and a time marching algorithm to couple the models. The whole strategy results from the transition between the microscopie model (Boltzmann) and the macroscopie model (Navier-Stokes). In order to generalize this adaptative coupling, we study this connection for diatomic gases. Finally, we justify the coupled problem from a mathematical view point
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds averaged Navier-Stokes equations." München Verl. Dr. Hut, 2007. http://d-nb.info/988422433/04.
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Benson, D. J. A. "Finite volume solution of Stokes and Navier-Stokes equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302883.
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Allaire, Grégoire. "Homogénéisation des équations de Stokes et de Navier-Stokes." Paris 6, 1989. http://www.theses.fr/1989PA066010.
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On étudie l'homogénéisation des équations de Stokes et Navier-Stokes avec une condition aux limites de Dirichlet dans un domaine contenant de petits obstacles, qui sont d'abord supposes répartis aux noeuds d'un réseau régulier périodique. On démontre la convergence du procédé d'homogénéisation lorsque le pas du réseau tend vers zéro. On étudie le probleme homogénéisé suivant la taille des obstacles
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Sahin, Pinar. "Navier-stokes Calculations Over Swept Wings." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607618/index.pdf.
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In this study, the non-equilibrium Johnson and King Turbulence Model (JK model) is implemented in a three-dimensional, Navier-Stokes flow solver. The main program is a structured Euler/Navier-Stokes flow solver in which spatial discretization is accomplished by a finite volume formulation and a multigrid technique is used as a convergence accelerator. The aim is the validation of this in-house developed CFD (Computational Fluid Dynamics) tool with this enhanced enlarged capability in order to obtain a reliable flow solver that can solve flows over swept wings accurately. Various test cases were evaluated against reference solutions in order to demonstrate the accuracy of the newly implemented JK turbulence model. The selected test cases are NACA 0012 airfoil, ONERA M6 wing, DLR-F4 wing and two wings taken from the 3rd Drag Prediction Workshop. The solutions were analyzed and discussed in detail. The results show appreciably good agreement with the experimental data including force coefficients and surface pressure distributions.
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Shuttleworth, Robert. "Block preconditioning the Navier-Stokes equations." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7002.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Gwilliam, Catherine Sarah. "Parallel algorithms for Navier-Stokes modelling." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357478.
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Lysov, Vyacheslav. "From Petrov-Einstein to Navier-Stokes." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11656.
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The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics.<br>Physics
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Neklyudov, Mikhail. "Navier-Stokes equations and vector advection." Thesis, University of York, 2006. http://etheses.whiterose.ac.uk/11011/.
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Patni, Kavita. "Damped Navier-Stokes equation in 2D." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/809731/.
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The main object to study in this thesis is the so-called damped and driven Navier-Stokes equations. These equations differ from the classical Navier-Stokes system by the presence of the extra damping term which is greater than zero, which is often referred to as the Ekman damping term and models the bottom friction in two-dimensional oceanic models.
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Albanez, Débora Aparecida Francisco 1984. "Continuous data assimilation for Navier-Stokes-alpha model = Assimilação contínua de dados para o modelo Navier-Stokes-alpha." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306185.
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Orientadores: Milton da Costa Lopes Filho, Helena Judith Nussenzveig Lopes<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-25T00:41:15Z (GMT). No. of bitstreams: 1
Albanez_DeboraAparecidaFrancisco_D.pdf: 3117782 bytes, checksum: 4f8e30c3d217ed3a6d26e9924d4df7ab (MD5)
Previous issue date: 2014<br>Resumo: Motivados pela existênca de um número finito de parâmetros determinantes (graus de liberdade), tais como modos, nós e médias espaciais locais para sistemas dinâmicos dissipativos, principalmente as equações de Navier-Stokes, apresentamos nesta tese um novo algoritmo de assimilação contínua de dados para o modelo tridimensional das equações Navier-Stokes-alpha, o qual consiste na introdução de um tipo geral de operador interpolante de aproximação (construído a partir de medições observacionais) dentro das equações de Navier-Stokes-alpha. O principal resultado garante condições sob a resolução espacial de dimensão finita dos dados coletados, suficientes para que a solução aproximada, construída a partir desses dados coletados, convirja para a referente solução que não conhecemos (realidade física) no tempo. Essas condições são dadas em termos de alguns parâmetros físicos, tais como a viscosidade cinemática, o tamanho do domínio e o termo de força<br>Abstract: Motivated by the presence of the finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, specially Navier-Stokes equations, we present in this thesis a new continuous data assimilation algorithm for the three-dimensional Navier-Stokes-alpha model, which consists of introducing a general type of approximation interpolation operator, (that is constructed from observational measurements), into the Navier-Stokes-alpha equations. The main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkwown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of the domain and the forcing term<br>Doutorado<br>Matematica<br>Doutora em Matemática
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Tryggeson, Henrik. "Analytical vortex solutions to Navier-Stokes equation." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1282.
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Fluid dynamics considers the physics of liquids and gases. This is a branch of classical physics and is totally based on Newton's laws of motion. Nevertheless, the equation of fluid motion, Navier-Stokes equation, becomes very complicated to solve even for very simple configurations. This thesis treats mainly analytical vortex solutions to Navier-Stokes equations. Vorticity is usually concentrated to smaller regions of the flow, sometimes isolated objects, called vortices. If one are able to describe vortex structures exactly, important information about the flow properties are obtained. Initially, the modeling of a conical vortex geometry is considered. The results are compared with wind-tunnel measurements, which have been analyzed in detail. The conical vortex is a very interesting phenomenaon for building engineers because it is responsible for very low pressures on buildings with flat roofs. Secondly, a suggested analytical solution to Navier-Stokes equation for internal flows is presented. This is based on physical argumentation concerning the vorticity production at solid boundaries. Also, to obtain the desired result, Navier-Stokes equation is reformulated and integrated. In addition, a model for required information of vorticity production at boundaries is proposed. The last part of the thesis concerns the examples of vortex models in 2-D and 3-D. In both cases, analysis of the Navier-Stokes equation, leads to the opportunity to construct linear solutions. The 2-D studies are, by the use of diffusive elementary vortices, describing experimentally observed vortex statistics and turbulent energy spectrums in stratified systems and in soapfilms. Finally, in the 3-D analysis, three examples of recent experimentally observed vortex objects are reproduced theoretically. First, coherent structures in a pipe flow is modeled. These vortex structures in the pipe are of interest since they appear for Re in the range where transition to turbulence is expected. The second example considers the motion in a viscous vortex ring. The model, with diffusive properties, describes the experimentally measured velocity field as well as the turbulent energy spectrum. Finally, a streched spiral vortex is analysed. A rather general vortex model that has many degrees of freedom is proposed, which also may be applied in other configurations.
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Inubushi, Masanobu. "Covariant Lyapunov Analysis of Navier-Stokes Turbulence." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/175095.
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Al-Jaboori, Mustafa Ali Hussain. "Navier-Stokes equations on the β-plane". Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5582/.
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Mathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy.
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Ngom, Evrad Marie Diokel. "Contrôle frontière des équations de Navier-Stokes." Phd thesis, Université Claude Bernard - Lyon I, 2014. http://tel.archives-ouvertes.fr/tel-01064942.
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Cette thèse est consacrée à l'étude de problèmes de stabilisation exponentielle par retour d'état ou "feedback" des équations de Navier-Stokes dans un domaine borné Ω ⊂ Rd, d = 2 ou 3. Le cas d'un contrôle localisé sur la frontière du domaine est considéré. Le contrôle s'exprime en fonction du champ de vitesse à l'aide d'une loi de feedback non-linéaire. Celle-ci est fournie grâce aux techniques d'estimation a priori via la procédure de Faedo-Galerkin laquelle consiste à construire une suite de solutions approchées en utilisant une base de Galerkin adéquate. Cette loi de feedback assure la décroissance exponentielle de l'énergie du problème discret correspondant et grâce au résultat de compacité, nous passons à la limite dans le système satisfait par les solutions approchées. Le chapitre 1 étudie le problème de stabilisation des équations de Navier- Stokes autour d'un état stationnaire donné, tandis que le chapitre 2 examine le problème de stabilisation autour d'un état non-stationnaire prescrit. Le chapitre 3 est consacré à l'étude de la stabilisation du problème de Navier-Stokes avec des conditions aux bords mixtes (Dirichlet- Neumann) autour d'un état d'équilibre donné. Enfin, nous présentons dans le chapitre 4, des résultats numériques dans le cas d'un écoulement autour d'un obstacle circulaire
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Haddon, E. W. "Numerical studies of the Navier-Stokes equations." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377745.
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Tang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.
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Hachicha, Imène. "Approximations hyperboliques des équations de Navier-Stokes." Thesis, Evry-Val d'Essonne, 2013. http://www.theses.fr/2013EVRY0015/document.
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Dans cette thèse, nous nous intéressons à deux approximations hyperboliques des équations de Navier-Stokes incompressibles en dimensions 2 et 3 d'espace. Dans un premier temps, on considère une perturbation hyperbolique de l'équation de la chaleur, introduite par Cattaneo en 1949, pour remédier au paradoxe de la propagation instantanée de cette équation. En 2004, Brenier, Natalini et Puel remarquent que la même perturbation, qui consiste à rajouter ε∂tt à l'équation, intervient en relaxant les équations d'Euler. En dimension 2, les auteurs montrent que, pour des sonnées régulières et sous certaines hypothèses de petitesse, la solution globale de la perturbation converge vers l'unique solution globale de (NS). En 2007, Paicu et Raugel améliorent les résultats de [BNP] en étendant la théorie à la dimension 3 et en prenant des données beaucoup moins régulières. Nous avons obtenu des résultats de convergence, avec données de régularité quasi-critique, qui complètent et prolongent ceux de [BNP] et [PR]. La seconde approximation que l'on considère est un nouveau modèle hyperbolique à vitesse de propagation finie. Ce modèle est obtenu en pénalisant la contrainte d'incompressibilité dans la perturbation de Cattaneo. Nous démontrons que les résultats d'existence globale et de convergence du précédent modèle sont encore vérifiés pour celui-ci<br>In this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one
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Słomka, Jonasz. "Generalized Navier-Stokes equations for active turbulence." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117861.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 211-227).<br>Recent experiments show that active fluids stirred by swimming bacteria or ATPpowered microtubule networks can exhibit complex flow dynamics and emergent pattern scale selection. Here, I will investigate a simplified phenomenological approach to 'active turbulence', a chaotic non-equilibrium steady-state in which the solvent flow develops a dominant vortex size. This approach generalizes the incompressible Navier-Stokes equations by accounting for active stresses through a linear instability mechanism, in contrast to externally driven classical turbulence. This minimal model can reproduce experimentally observed velocity statistics and is analytically tractable in planar and curved geometry. Exact stationary bulk solutions include Abrikosovtype vortex lattices in 2D and chiral Beltrami fields in 3D. Numerical simulations for a plane Couette shear geometry predict a low viscosity phase mediated by stress defects, in qualitative agreement with recent experiments on bacterial suspensions. Considering the active analog of Stokes' second problem, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. The model readily generalizes to curved geometries. On a two-sphere, we present exact stationary solutions and predict a new type of upward energy transfer mechanism realized through the formation of vortex chains, rather than the merging of vortices, as expected from classical 2D turbulence. In 3D simulations on periodic domains, we observe spontaneous mirror-symmetry breaking realized through Beltrami-like flows, which give rise to upward energy transfer, in contrast to the classical direct Richardson cascade. Our analysis of triadic interactions supports this numerical prediction by establishing an analogy with forced rigid body dynamics and reveals a previously unknown triad invariant for classical turbulence.<br>by Jonasz Słomka.<br>Ph. D.
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Silva, Felipe Wallison Chaves. "Controlabilidade para o sistema de Navier-Stokes." Universidade Federal da Paraíba, 2009. http://tede.biblioteca.ufpb.br:8080/handle/tede/7452.
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Made available in DSpace on 2015-05-15T11:46:23Z (GMT). No. of bitstreams: 1
arquivototal.pdf: 490053 bytes, checksum: c9cf689fde66aed86d7eb372eeb05045 (MD5)
Previous issue date: 2009-05-15<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Cook's local infuence approach based on normal curvature is an important diagnostic tool
for assessing local infuence of minor perturbations to a statistical model. However, no rigorous
approach has been developed to address two fundamental issues: the selection of an appropriate
perturbation and the development of infuence measures for objective functions at a point with a
nonzero
first derivative. The aim of this paper is to develop a diferential-geometrical framework of
a perturbation model (called the perturbation manifold) and utilize associated metric tensor and
affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation
manifold provides important information about selecting an appropriate perturbation of a model.<br>Esta dissertação é dedicada ao estudo do sistema de Navier-Stokes sob ponto
de vista da teoria do controle. Primeiramente estudamos a controlabilidade das
aproximações de Galerkin do sistema de Navier-Stokes. Utilizando argumentos de
dualidade e de ponto fixo, mostramos que, com hipóteses adequadas sobre a base
de Galerkin, estas aproximações, finito dimensionais, são exatamente controláveis.
Passando ao modelo em dimensão infinita, analisamos a controlabilidade sobre trajetórias. Isto é feito usando uma desigualdade do tipo Calerman para o sistema de
Navier-Stokes linearizado e uma versão do teorema da função inversa. Dessa forma,
temos um resultado de controlabilidade local exata para o sistema de Navier-Stokes.
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Drouet, Aurélien. "Apports de la résolution multi-blocs pour la simulation de la manoeuvrabilité des sous-marins et des bâtiments de surface." Ecole centrale de Nantes, 2011. http://www.theses.fr/2011ECDN0045.
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L'estimation des performances manoeuvrières d'un navire est une étape indispensable pour garantir la sécurité d'un navire, de ses occupants et de tout ce qui l'entoure (environnement, autres navires). L'objectif de cette thèse est d'adapter un code de calcul Navier-Stokes à surface libre afin de simuler numériquement des manoeuvres de sous-marins ou de bâtiments de surface. Les premiers chapitres de ce manuscrit sont consacrés à la définition des équations de Navier-Stokes, à leur linéarisation puis à leur discrétisation, necéssaire à leur utilisation numérique. Un bref chapitre présente ensuite les différents types de topologies de maillages et expose les premiers avantages de l'utilisation de maillages multi-blocs. Les modifications apportées au code de calcul afin de prendre en compte cette nouvelle topologie de maillage sont ensuite présentées avec leurs validations associées. L'ensemble des fonctionnalités nécessaires à la simulation d'un navire autopropulsé en manoeuvre est ensuite détaillé. Le code de calcul étant voué à une utilisation industrielle, le temps de restitution des résultats doit être relativement faible. Ainsi, une description des phases d'optimisation et de parallélisation effectuées sur le code initial mono-bloc est décrite. Enfin, les deux derniers chapitres présentent, d'une part une validation effectuée sur un cas test de sous-marin (DARPA SUBOFF) sur une large gamme de configurations modèle bridé en comparaison à des valeurs de coefficients hydrodynamiques issus d'essais expérimentaux, et d'autre part des applications de manoeuvrabilité de navire (sous-marins ou bâtiment de surface) autopropulsé modèle libre (remontée feuille morte, giration, zigzag)<br>Estimating the performances of ship maneuverability is a necessary stage to guarantee the safety of the crew and of the surrounding environment. The objective of this PhD thesis is to adapt a free surface Navier-Stokes computational code in order to be used for a submarine or ship maneuverability modeling. The first chapters are dedicated to the definition of Navier-Stockes equations and their linearization and discretization that are used for the numerical scheme. Then, a brief chapter presents the different mesh topologies and advantages of using the multi-block meshing approach. The developments implemented into the code to take into account this innovating meshing topology are presented, as well as a the associated validation test cases. The overall functionabilities needed for an auto-propulled maneuvering ship are then detailed. The CPU time must be relatively low since the numerical code is dedicated to an industrial use. Hence, a description of optimization and parallelization stages performed on the initial single-block code is described. To conlude, the two last chapters present a validation test case end possible industrial applications enable by the developments performed. The validation test case is performes on a submarine (DARPA SUBOFF) on a wide range of fixed model configurations, and results are compared to experimental hydrdynamic coefficient. Possible configurations of submarine or ship maneuverability in auto-propolled and free model configurations are presented, such as turning cricle maneuver, pullout, zigzag. .
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De, Santis Dante. "Schémas d'ordre élevé distribuant le résidu pour la résolution des équations de Navier-Stokes et Navier-Stokes moyennées (RANS)." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00935419.
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Cette thèse présente la construction de schémas distribuant le résidu (RD) d'ordre très élevés, pour la discrétisation d'équations d'advection-diffusion multidimensionnelles et stationnaires sur maillages non structurés. Des schémas linéaires ainsi que des schémas non linéaires sont considérés. Une approximation de la solution polynomiale par morceaux et continue sur chaque élément est adoptée, de plus une procédure de reconstruction du gradient que celle de la solution numérique est utilisée afin d'avoir une représentation continue de la solution numérique et de son gradient. Il est montré que le gradient doit être reconstruit avec la même précision de la solution, sans quoi la précision formel du schéma numérique est perdue dans les cas où les effets de diffusion prévalent sur les effets d'advection, et aussi quand l'advection et la diffusion sont également importants. Ensuite, la méthode est étendue à des systèmes d'équations, en particulier aux équations de Navier-Stokes et aux équations RANS. La précision, l'efficacité et la robustesse du solveur RD implicite sont démontrées sur plusieurs cas tests.
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Barrère, Jean. "Modélisation des écoulements de Stokes et Navier-Stokes en milieux poreux." Bordeaux 1, 1990. http://www.theses.fr/1990BOR10516.
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On etudie le passage d'ecoulements microscopiques a l'echelle du pore, regis par les equations de stokes et de navier-stokes, aux ecoulements macroscopiques dans un milieu poreux, regis par la loi de darcy. Les principaux points d'etudes sont: le passage en revue des theories de prise de moyenne et l'etablissement de l'equivalence de celles-ci et la theorie d'homogeneisation dans le cas de milieux periodiques, la determination numerique par une methode aux differences finies, de tenseurs de permeabilite dans des milieux periodiques anisotropes tridimensionnels, l'etude numerique, par une methode aux elements finis, des non-linearites en regime de navier-stokes dans un treillis de cylindres. La loi macroscopique d'ecoulement obtenue fait intervenir une expression cubique de la vitesse de filtration
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Wachsmuth, Daniel. "Optimal control of the unsteady Navier-Stokes equations." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982143419.
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Jiang, Ning. "Weakly compressible Navier-Stokes approximation of gas dynamics." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3883.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.<br>Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Liu, Jie. "A class of efficient, stable Navier-Stokes solvers." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3695.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.<br>Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.
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Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
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Grira, Sofiane. "Les équations de Navier-Stokes nonlinéaires dans IR³." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ26576.pdf.
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Li, Ming. "Numerical solutions for the incompressible Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0016/NQ37725.pdf.
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Litton, Daniel. "Algorithmic Enhancements to the VULCAN Navier-Stokes Solver." NCSU, 2003. http://www.lib.ncsu.edu/theses/available/etd-08132003-230354/.
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VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M < 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can accurately solve the Navier-Stokes equations for very low Mach numbers.
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Sommerville, Lesley Laverne. "A Parabolized navier-stokes model for static mixers." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/19535.
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Li, Yuhong. "Asymptotical behaviour of 2D stochastic Navier-Stokes equations." Thesis, University of Hull, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411901.
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Osborne, Daniel. "Navier-Stokes equations and stochastic models of turbulence." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497064.
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Ryou, H. S. "Viscous/inviscid matching using imbedded Navier/Stokes equations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47236.
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Schäfer, Christian Thomas. "Elastohydrodynamic lubrication based on the Navier-Stokes equations." Thesis, Liverpool John Moores University, 2005. http://researchonline.ljmu.ac.uk/5788/.
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Newman, Christopher K. "Exponential Integrators for the Incompressible Navier-Stokes Equations." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/29340.
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We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size.
Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step.
Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L2 inner product. We examine this L2 projection and an H1 projection induced by the H1 semi-inner product. The H1 projection has an advantage over the L2 projection in that it retains tangential Dirichlet boundary conditions for the flow. Both the H1 and L2 projections are solutions to saddle point problems that are efficiently solved by a preconditioned Uzawa algorithm.<br>Ph. D.
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Zahed, Hanadi. "Computation of bifurcations for the Navier-Stokes equations." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/computation-of-bifurcations-for-the-navierstokes-equations(6f5f55ac-0379-495b-8652-7baaeb117a4b).html.
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We investigate a two-dimensional boundary layer flow in a channel with a suction slot on the upper wall by solving the steady Navier-Stokes equations to compute steady state solutions and we investigate their stability using global stability analysis together with linear temporal simulation and a continuation method. Our primary aim in this work is to investigate bifurcations occurring in separated flows at large Reynolds numbers (R). Another motivation is to investigate the stability of a separated flow. The 2D steady Navier-Stokes equations in stream function(ψ)-vorticity (ω) are solved numerically using a hybrid finite difference and spectral method combined with pseudo arc length continuation techniques to track turning points and bifurcations. We are able to calculate two branches of solutions and the turning point bifurcation in this particular problem. Global stability results indicate that the first solution on the lower branch, where the separation bubble is short, is stable, while the second solution on the upper branch, where the separation bubble is large, is unstable. The presence of the turning point is confirmed by the changing signs in the eigenvalue spectrum, as it moves from the lower, stable solution branch to the upper, unstable solution branch. The numerical simulation confirms the stability of the lower branch solutions and confirms that the upper branch is unstable; it is also in good agreement with global stability behaviour.
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Montoya, Zambrano Cristhian David. "Inverse source problems and controllability for the stokes and navier-stokes equations." Tesis, Universidad de Chile, 2016. http://repositorio.uchile.cl/handle/2250/141346.
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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática<br>This thesis is focused on the Navier{Stokes system for incompressible
uids with either
Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some
ideas in the context of the control theory and inverse source problems. The thesis is divided
in three parts.
In the rst part, we deal with the local null controllability for the Navier{Stokes system
with nonlinear Navier{slip conditions, where the internal controls have one vanishing component.
The novelty of the boundary conditions and the new estimates with respect to the
pressure term, has allowed us to extend previous results on controllability for the Navier{
Stokes system. The main ingredients to build our result are the following: a new regularity
result for the linearized system around the origin, and a suitable Carleman inequality for the
adjoint system associated to the linearized system. Finally, xed point arguments are used
in order to conclude the proof.
In the second part, we deal with an inverse source problem for the N- dimensional Stokes
system from local and missing velocity measurements. More precisely, our main result establishes
a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of
N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function,
meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable
Sobolev space. The main tools are the following: connection between null controllability and
inverse problems throughout a result on null controllability for the N- dimensional Stokes
system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral
equations. We also implement this result and present several numerical experiments
that show the feasibility of the proposed recovering formula.
Finally, the last chapter of the thesis presents a partial result of stability for the Stokes
system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial
function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for
solving inverse problems and some topics in degenerate Sobolev spaces.
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Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.
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Al, Baba Hind. "Théorie des semi-groupes pour les équations de Stokes et de Navier-Stokes avec des conditions aux limites de type Navier." Thesis, Pau, 2015. http://www.theses.fr/2015PAUU3008/document.
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Cette thèse est consacrée à l'étude théorique mathématique des équations de Stokes et de Navier-Stokes dans un domaine borné de R^3 en utilisant la théorie des semi-groupes. Trois différents types de conditions seront considérés : des conditions aux limites de Navier, de type-Navier et des conditions qui dépendent de la pression. Ce manuscrit est composé de six chapitres. Tout d'abord nous commençons par un état de l'art sur les équations de Navier-Stokes. Ensuite nous démontrons l'analyticité du semi-groupe de Stokes avec chacune des conditions ci-dessus. Ceci permet de résoudre le problème d'évolution en utilisant la théorie des semi-groupes. Nous étudions également les puissances complexes et fractionnaires de l'opérateur de Stokes pour lesquelles nous démontrons certaines propriétés et estimations. Ces résultats seront utilisés dans la suite pour obtenir des estimations de type L^p-L^q pour le semi-groupe de Stokes, un résultat de régularité L^p-L^q maximale pour le problème de Stokes inhomogène et des résultats d'existence et d'unicité locale pour le problème non-linéaire. Après nous étudions le problème d'évolution de Stokes. Outre la régularité L^p-L^q maximale, nous démontrons l'existence des solutions faibles u∈L^q (0,T; W^(1,p) (Ω)), fortes u∈L^q (0,T; W^(2,p) (Ω)) et très faibles u∈L^q (0,T; L^p (Ω)) du problème de Stokes. On termine par l'étude du problème de Navier-Stokes avec chacune des conditions aux limites citées ci-dessus. Tout d'abord, en utilisant les estimations L^p-L^q on démontre l'existence d'une unique solution locale u qui vérifieu∈BC([0,T_0 ); L_(σ,τ)^p (Ω))∩L^q (0,T_0; L_(σ,τ)^r (Ω)), q,r>p, 2/q+3/r=3/p.De plus, pour une donnée initiale petite, on obtient l'existence globale des solutions. Ensuite en estimant le terme non-linéaire en fonction des puissances fractionnaires de l'opérateur de Stokes on démontre la régularité de la solution<br>This thesis is devoted to the mathematical theoretical study of the Stokes and Navier-Stokes equations in a bounded domain of R^3 using the semi-group theory. Three different types of boundary conditions will be considered: Navier boundary conditions, Navier-type boundary conditions and boundary condition involving the pressure. This manuscript contains six chapters. We prove first the analyticity of the Stokes semi-group with each of the boundary conditions stated above. This allows us to solve the time dependent Stokes problem using the semi-group theory. We will study also the complex and fractional powers of the Stokes operator for which we prove some properties and estimations. These results will be used in the sequel to prove an estimate of type L^p-L^q for the Stokes semigroup, as well as the maximal L^p-L^q regularity for the inhomogeneous Stokes problem and an existence result for the non-linear problem. Next we study the time dependent Stokes problem, besides the maximal L^p-L^q regularity, we prove the existence of weak u∈L^q (0,T; W^(1,p) (Ω)), strong u∈L^q (0,T; W^(2,p) (Ω)) and very weak u∈L^q (0,T; L^p (Ω)) solutions to the Stokes problem. We end with the study of the Navier-Stokes problem. First using the L^p-L^q estimate for the Stokes semi-group we prove the existence of a unique local in time mild solution for the Navier-Stokes problem that verifies u∈BC([0,T_0 ); L_(σ,τ)^p (Ω))∩L^q (0,T_0; L_(σ,τ)^r (Ω)), q,r>p, 2/q+3/r=3/p.Furthermore, for some initial data the solution is global in time. Finally, by estimating the non-linear term as a function of the fractional powers of the Stokes operator we prove that the solution is regular
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Guzzo, Sandro Marcos. "Estudo de equações do tipo Navier-Stokes com retardo." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-01092009-105829/.
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Neste trabalho estudamos a existência de soluções de equações do tipo Navier-Stokes com retardo na força externa e no termo n~ao linear. Usando a teoria de semigrupos estudamos a existência de soluções para um problema da forma \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), em \'OMEGA\' x (0, T), div u(t) = 0 em \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x PERTENCE a \' OMEGA\', u(t, x) = 0 t > 0, X \'PERTENCE A\' \' PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'PERTENCE A\' (- \'INFINITO\', 0) x \'PERTENCE A\' \'OMEGA\', onde F9t, \'uIND.t) = INT.IND.t SUP. -\' INFINITO\' \' ALFA1(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITO \'BETA\' (s-t)u(s)ds. Similarmente, usando a tecnica de aproximac~oes de Galerkin, estudamos o problema anterior com F(.) e g(.) dadas por f(t; \'u INDS.t\') = u(t-r(t)); e g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), para alguma função G apropriada. Neste caso, também estudamos a estabilidade de soluções estacionarias<br>In this work we stuy the existence of solutions for a Navier-Stokes typt equations with delay in the external force and in the nonlinear term. Using the semi-group theory we study the existence of solution for a problem in the form \'d. SUP. dt u(t) - v\'delta\'u(t) + (F(t, \'u IND.t\'). abla)u(t) + abla p = g(t, \'u IND.t\'), ijn \'OMEGA\' x (0, T), div u(t) = 0 in \'OMEGA\' x (0, T), u(0, x) = \'u POT.0 (x) x \'IT BELONGS \' OMEGA\', u(t, x) = 0 t > 0, X \'IT BELONGS\' \'PARTIAL\' \'OMEGA\', u(t, x) =\\phi (t, x) t \'IT BELONGS\' (- \'INFINITY\', 0) x \'IT BELONGS\' \'OMEGA\', where F(t, \'u .t) = INT.IND.t SUP. -\' INFINITY\' \' ALFA(s-t)u(s)ds + u(t-r), g(t, \'u IND.t\') = INT. SUP. t IND. - INFINITY \'BETA\' (s-t)u(s)ds. On another hand using the Galerkin appreoximations method we study the same with F(.) e g(.) given by f(t; \'u INDS.t\') = u(t-r(t)); and g(t; \'u IND.t\') = G(u(t-\'rô\' (t))), for some G appropriated. In thiis case, we study also the stability of stanionary solutions
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Yung, Hoi Yan Ada, and 翁凱欣. "On block preconditioners for the incompressible Navier-Stokes equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44907138.
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